Gina Rinehart's son, John Hancock, has withdrawn his application to replace her as head of a controversial family trust, standing behind his sister Bianca Rinehart to run the trust in the "interests of family harmony".

The court heard Ms Rinehart is willing to take on the role, and that the support of billionaire Andrew Forrest for Mr Hancock to take on the role will no longer be needed.

In a statement, Mr Hancock said: "I made the decision last night to ask Bianca to nominate as replacement trustee."

However, Ms Rinehart's younger sister, Ginia Rinehart, opposes her taking up the appointment.

Ginia Rinehart's lawyer, Richard McHugh, told the court: "If the plaintiffs wanted to have Bianca as trustee, they should have said so months ago."

As a result, a long-awaited civil trial started on Wednesday, involving two of Mrs Rinehart's children - Mr Hancock and Bianca Rinehart - who accuse her of misconduct as a trustee.

They allege she deceived them and was dishonest about the trust, which was set up by her father Lang Hancock in 1988 with her children as beneficiaries.

They also want Justice Paul Brereton to rule that changes their mother made in 2006 to a constitution governing the affairs of the trust are invalid.

The changes stipulated that any future trustee should be Mrs Rinehart's direct descendant and that her children should sign prenuptial agreements to stop non-family members acquiring shares in Hancock Prospecting, Australia's largest private company.

The trust owns about a quarter of the company.

Mrs Rinehart denies their allegations and maintains she has always acted in her children's best interests.

The case against her was first lodged in September 2011 when the trust was due to vest.

Another of her children, Hope Welker, at first sided with Mr Hancock and Bianca Rinehart but has since dropped out.

Ginia Hancock has sided with her mother from the beginning.

Over the past two years Mrs Rinehart has lost several court cases to try to have the dispute kept out of open court.

When her lawyer Bruce McClintock last week announced she was willing be discharged as trustee he noted that a lot of her time has been taken up with "unnecessary litigation."